Objectives:

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As an IB Learner you are reflective. On your own page of your blog you will need to explain each of these important ideas in your own words:

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TYPES OF QUESTIONS TO SOLVE:

• Describe the limit process, including Zeno's paradox.

• Describe the derivative, including the tangent problem.

• Describe the integral, including the area problem.

• Be able to guess the limit of a sequence.

• Be able to draw the line tangent to a curve at a specified point.

• Approximate an area by using rectangles.

• Explain the process of mathematical modeling.

• Write out the first 5 terms of a sequence when given a general term.

• Find the limit of a sequence.

• Solve applied problems involving limits of sequences.

• Estimate a rate of change by looking at a graph.

• Estimate the slope of a tangent line by looking at a graph.

• Find an average rate of change for a given function over an interval.

• Find an instantaneous rate of change for a given function at a particular point.

• Find the derivative by using the definition of derivative.

• Find the equation of a tangent line.

• Evaluate an area function.

• Find an antiderivative.

• Find the area under a curve.

• Approximate the value of a definite integral by using areas.

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What is Calculus?

Isaac Newton:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Newton.html



Gottfried Leibniz:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Leibniz.html

Reference Topic Sites:

http://www.brightstorm.com/math/calculus/

"The limit"
"Archimedes' calculation of pi"
"Secants and tangents"
http://www.math.psu.edu/dna/graphics.html

Discussions on Zeno's paradox:
http://mathforum.org/isaac/problems/zeno1.html

Article on mathematical modeling and why it is important:
http://www.mtholyoke.edu/courses/jmorrow/math_models.html

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Limits

Video:

Introduction to the limit of a function (time: 8:44)

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Derivatives

Video:

Introduction to derivative (time: 8:44)

Reference Topic Sites:

Check out the following on this site:
"Secants and tangents"
"Zooming in on a tangent line"
http://www.math.psu.edu/dna/graphics.html

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Integrals

Reference Topic Sites:

Check out "Archimedes' calculation of pi" on this site:
http://www.math.psu.edu/dna/graphics.html